Theorems · Theorem · group theory
commutator_eq_closure
∀ (G : Type u_1) [inst : Group G], commutator G = Subgroup.closure (commutatorSet G)
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- Subgroupstatement · cited by 3,593
- Bracket.bracketproof · cited by 642
- Subgroup.closurestatement and proof · cited by 196
- commutatorstatement · cited by 56
- commutatorSetstatement · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- Abelianization.commutator_subset_kerproof · cited by 5
- Subgroup.Normal.quotient_commutative_iff_commutator_leproof · cited by 2
- Subgroup.rank_commutator_le_cardproof · cited by 1
- alternatingGroup.commutator_perm_leproof · cited by 1
- Equiv.Perm.IsThreeCycle.mem_commutator_alternatingGroupproof · cited by 1
- card_commutator_closureCommutatorRepresentativesproof · cited by 1
- IsSimpleGroup.comm_iff_isSolvableproof · cited by 0